Jacobi's condition for singular extremals: An extended notion of conjugate points (Q1861787)

In the theory of the calculus of variations, for the so-called fixed endpoint problem, Jacobi's necessary condition for the optimality (of a nonsingular trajectory) states that there are no conjugate points in the interior of the underlying time interval. By extending the notion of conjugate points, the authors verify the above necessary condition also for all (that is, also for singular) trajectories, thus, the result of this paper fulfills a gap in the theory. An example illustrating the usefulness of this result is offered as well.